Sensitive particle detection with spatially-varying polarization rotator and polarizer

ABSTRACT

A system may include illumination optics to direct an illumination beam to a sample at an off-axis angle, collection optics to collect scattered light from the sample, and a phase mask located at a first pupil plane to provide different phase shifts for light in two or more pupil regions of a collection area to reshape a point spread function of light scattered from one or more particles on a surface of the sample. The system may further include a polarization rotator located at a second pupil plane, where the polarization rotator provides a spatially-varying polarization rotation angle selected to rotate light scattered from the surface of the sample to a selected polarization angle, a polarizer to reject light polarized along the selected polarization angle, and a detector to generate a dark-field image of the sample based on light passed by the polarizer.

CROSS-REFERENCE TO RELATED APPLICATION

The present application is related to and claims benefit of the earliestavailable effective filing date from the following applications. Thepresent application constitutes a continuation application of U.S.patent application Ser. No. 16/577,326, filed on Sep. 20, 2019, which isa regular (non-provisional) patent application claiming the benefit ofU.S. Provisional Patent Application Ser. No. 62/806,820, filed Feb. 17,2019, whereby each of the above-listed patent applications isincorporated herein by reference in their entirety.

TECHNICAL FIELD

The present disclosure is generally related to particle inspection and,more particularly, to particle inspection using dark-field imaging basedon scattered or diffracted light.

BACKGROUND

Particle detection systems are commonly utilized in semiconductorprocessing lines to identify defects or particulates on wafers such as,but not limited to, unpatterned wafers. As semiconductor devicescontinue to shrink, particle detection systems require correspondingincreases in sensitivity and resolution. A significant source of noisethat may limit measurement sensitivity is surface scattering on a wafer(e.g., surface haze), which may be present even for optically polishedsurfaces. While various methods have been proposed to suppress surfacescattering with respect to scattering from particles, such methods mayfail to achieve desired sensitivity levels and/or may achievesensitivity at the expense of degraded image quality. There is thereforea need to develop systems and methods that mitigate the deficienciesaddressed above.

SUMMARY

A system is disclosed in accordance with one or more illustrativeembodiments of the present disclosure. In one illustrative embodiment,the system includes an illumination source to generate an illuminationbeam. In another illustrative embodiment, the system includes one ormore illumination optics to direct the illumination beam to a sample atan off-axis angle along an illumination direction. In anotherillustrative embodiment, the system includes one or more collectionoptics to collect scattered light from the sample in response to theillumination beam in a dark-field mode. In another illustrativeembodiment, the system includes a phase mask located at a first pupilplane of the one or more collection optics, where the phase mask isconfigured to provide different phase shifts for light in two or morepupil regions of a collection area to reshape a point spread function oflight scattered from one or more particles on a surface of the sample.In another illustrative embodiment, the collection area corresponds to anumerical aperture of the one or more collection optics. In anotherillustrative embodiment, the system includes a polarization rotatorlocated at a second pupil plane of the one or more collection optics,where the polarization rotator provides a spatially-varying polarizationrotation angle selected to rotate light scattered from the surface ofthe sample to a selected polarization angle. In another illustrativeembodiment, the polarization rotator includes an optically-activematerial with an optic axis oriented perpendicular to the second pupilplane that rotates a polarization of light in the second pupil planebased on optical activity, where the optically-active material has aspatially-varying thickness across the pupil plane to rotate the lightscattered from the surface of the sample to the selected polarizationangle. In another illustrative embodiment, the system includes apolarizer aligned to reject light polarized along the selectedpolarization angle. In another illustrative embodiment, the systemincludes a detector to generate a dark-field image of the sample basedon light passed by the polarizer, where the light passed by thepolarizer includes at least a portion of the light scattered by the oneor more particles on the surface of the sample.

An apparatus is disclosed in accordance with one or more illustrativeembodiments of the present disclosure. In one illustrative embodiment,the apparatus includes a polarization rotator providing aspatially-varying polarization rotation angle selected to rotate lightscattered from a surface of a sample to a selected polarization anglewhen the polarization rotator is placed in a pupil plane of an imagingsystem, where the light scattered from the surface of the samplepropagates through the polarization rotator along a thickness direction.In another illustrative embodiment, the polarization rotator includes anoptically-active material with an optic axis oriented along thethickness direction that rotates a polarization of light based onoptical activity, where the optically-active material has aspatially-varying thickness across a transverse direction orthogonal tothe thickness direction to rotate the light scattered from the surfaceof the sample to the selected polarization angle.

A system is disclosed in accordance with one or more illustrativeembodiments of the present disclosure. In one illustrative embodiment,the system includes an illumination source to generate an illuminationbeam. In another illustrative embodiment, the system includes one ormore illumination optics to direct the illumination beam to a sample atan off-axis angle along an illumination direction. In anotherillustrative embodiment, the system includes one or more collectionoptics to collect scattered light from the sample in response to theillumination beam in a dark-field mode. In another illustrativeembodiment, the system includes a phase mask located at a first pupilplane of the one or more collection optics, where the phase mask isconfigured to provide different phase shifts for light in two or morepupil regions of a collection area to reshape a point spread function oflight scattered from one or more particles on a surface of the sample.In another illustrative embodiment, the collection area corresponds to anumerical aperture of the one or more collection optics. In anotherillustrative embodiment, the system includes a polarization rotatorlocated at a second pupil plane of the one or more collection optics,wherein the polarization rotator provides a spatially-varyingpolarization rotation angle selected to rotate light scattered from thesurface of the sample to a selected polarization angle, where thepolarization rotator includes an angularly-segmented half-wave plateincluding a plurality of segments having edges oriented to intersect atan apex point in the second pupil plane. In another illustrativeembodiment, the apex point corresponds to specular reflection of theillumination beam in the second pupil plane. In another illustrativeembodiment, the system includes a polarizer aligned to reject lightpolarized along the selected polarization angle. In another illustrativeembodiment, the system includes a detector to generate a dark-fieldimage of the sample based on the light passed by the polarizer, wherethe light passed by the polarizer includes at least a portion of lightscattered by the one or more particles on the surface of the sample.

A system is disclosed in accordance with one or more illustrativeembodiments of the present disclosure. In one illustrative embodiment,the system includes an illumination source to generate an illuminationbeam. In another illustrative embodiment, the system includes one ormore illumination optics to direct the illumination beam to a sample atan off-axis angle along an illumination direction. In anotherillustrative embodiment, the system includes a detector. In anotherillustrative embodiment, the system includes one or more collectionoptics to generate a dark-field image of the sample on the detectorbased on light collected from the sample in response to the illuminationbeam. In another illustrative embodiment, the system includes a phasemask located at a pupil plane, where the phase mask is configured toprovide different phase shifts for light in two or more pupil regions ofa collection area to reshape a point spread function of light scatteredfrom one or more particles on a surface of the sample. In anotherillustrative embodiment, the collection area corresponds to a numericalaperture of the one or more collection optics. In another illustrativeembodiment, the system includes a linearly-segmented polarizer includinga plurality of segments distributed in a pupil plane of the one or morecollection optics along a segmentation direction, where a rejection axisof each segment is oriented to reject light scattered from the surfaceof the sample within the segment.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory onlyand are not necessarily restrictive of the invention as claimed. Theaccompanying drawings, which are incorporated in and constitute a partof the specification, illustrate embodiments of the invention andtogether with the general description, serve to explain the principlesof the invention.

BRIEF DESCRIPTION OF DRAWINGS

The numerous advantages of the disclosure may be better understood bythose skilled in the art by reference to the accompanying figures inwhich:

FIG. 1 is a conceptual view of a particle detection system, inaccordance with one or more embodiments of the present disclosure;

FIG. 2A is a pupil-plane scattering map of surface scattering inresponse to obliquely-incident p-polarized light, in accordance with oneor more embodiments of the present disclosure;

FIG. 2B is a pupil-plane scattering map of light scattered by asub-resolution particle in response to obliquely-incident p-polarizedlight, in accordance with one or more embodiments of the presentdisclosure;

FIG. 3A is a conceptual top view of a segmented polarizer havingwedge-shaped segments distributed radially around an apex location, inaccordance with one or more embodiments of the present disclosure;

FIG. 3B is a conceptual top view of a segmented polarizer in whichsegments are linearly distributed along a selected segmentationdirection in the pupil plane, in accordance with one or more embodimentsof the present disclosure;

FIG. 4 is a conceptual top view of a phase mask including two segmentsto divide the pupil into two segments, in accordance with one or moreembodiments of the present disclosure.

FIG. 5 is a conceptual top view of a polarization rotator formed as anangularly-segmented half-wave plate, in accordance with one or moreembodiments of the present disclosure;

FIGS. 6A and 6B are plots of orthogonally polarized portions of thecollected sample light after propagating through an angularly-segmentedpolarization rotator and a polarizing beamsplitter, in accordance withone or more embodiments of the present disclosure;

FIG. 7A is a conceptual top view of a polarization rotator formed as alinearly-segmented half-wave plate, in accordance with one or moreembodiments of the present disclosure;

FIG. 7B is a calculated plot of the orientation directions of the opticaxes of a linearly-segmented polarization rotator shown in FIG. 7A as afunction of position in the pupil plane along the segmentationdirection, in accordance with one or more embodiments of the presentdisclosure;

FIG. 7C is a plot of orientation directions for optic axes of alinearly-segmented polarization rotator to rotate the polarization ofsurface haze to a selected polarization angle, in accordance with one ormore embodiments of the present disclosure;

FIGS. 8A and 8B are plots of orthogonally polarized portions of thecollected sample light after propagating through an angularly-segmentedpolarization rotator and a polarizing beamsplitter, in accordance withone or more embodiments of the present disclosure;

FIG. 9A is an image of a particle smaller than a resolution of animaging system generated based on scattering of obliquely-incidentp-polarized light, in accordance with one or more embodiments of thepresent disclosure;

FIG. 9B includes an image of the particle in FIG. 8A using an imagingsystem with an angularly-segmented polarization rotator as illustratedin FIG. 5 and a polarizing beamsplitter, in accordance with one or moreembodiments of the present disclosure;

FIG. 9C includes an image of the particle in FIG. 9A using an imagingsystem with a linearly-segmented polarization rotator as illustrated inFIG. 7A with 72 segments and a linear polarizer, in accordance with oneor more embodiments of the present disclosure;

FIG. 10 is a plot illustrating the performance and convergence behaviorof an angularly-segmented polarization rotator and a linearly-segmentedpolarization rotator, in accordance with one or more embodiments of thepresent disclosure;

FIG. 11A is a plot of SNR as a function of pixel size for a segmentedpolarizer and a segmented polarization rotator using an illuminationbeam having a wavelength of 266 nm, in accordance with one or moreembodiments of the present disclosure;

FIG. 11B is a plot of SNR as a function of pixel size for a segmentedpolarizer and a segmented polarization rotator using an illuminationbeam having a wavelength of 213 nm, in accordance with one or moreembodiments of the present disclosure;

FIG. 12 is a conceptual top view of a polarization rotator formed froman optically-active material, in accordance with one or more embodimentsof the present disclosure;

FIG. 13A is a plot of a thickness profile along the vertical directionof FIG. 12 of a polarization rotator formed from an optically activematerial designed to rotate the polarization of surface haze havingwavelengths of 266 nm and 213 nm, respectively, to the horizontaldirection in FIG. 12, in accordance with one or more embodiments of thepresent disclosure;

FIG. 13B is a cross-sectional view of a polarization rotator having athickness profile based on FIG. 13A, in accordance with one or moreembodiments of the present disclosure;

FIG. 14A is a plot of a thickness profile along the vertical directionof FIG. 12 of a polarization rotator formed from an optically activematerial designed to rotate the polarization of surface haze havingwavelengths of 266 nm and 213 nm, respectively, to the horizontaldirection in FIG. 12, in accordance with one or more embodiments of thepresent disclosure;

FIG. 14B is a cross-sectional view of a polarization rotator having athickness profile based on FIG. 14A, in accordance with one or moreembodiments of the present disclosure; and

FIG. 15 is a flow diagram illustrating steps performed in a method forparticle detection, in accordance with one or more embodiments of thepresent disclosure.

DETAILED DESCRIPTION

Reference will now be made in detail to the subject matter disclosed,which is illustrated in the accompanying drawings. The presentdisclosure has been particularly shown and described with respect tocertain embodiments and specific features thereof. The embodiments setforth herein are taken to be illustrative rather than limiting. As usedherein, directional terms such as “left”, “right”, “top”, “bottom”,“over”, “under”, “upper”, “upward”, “lower”, “down” and “downward” areintended to provide relative positions for purposes of description, andare not intended to designate an absolute frame of reference. It shouldbe readily apparent to those of ordinary skill in the art that variouschanges and modifications in form and detail may be made withoutdeparting from the spirit and scope of the disclosure.

Embodiments of the present disclosure are directed to systems andmethods for particle detection based on dark-field imaging in whichsurface scattering (e.g., surface haze) is separated from lightscattered by particles on a surface (e.g., particle scattering).Additional embodiments of the present disclosure are directed tosimultaneously generating separate images of a sample based on surfacescattering and particle scattering.

Wafer inspection is generally described in U.S. Pat. No. 9,874,526issued on Jan. 1, 2018, U.S. Pat. No. 9,291,575 issued on Mar. 22, 2016,U.S. Pat. No. 8,891,079 issued on Nov. 18, 2014, and U.S. Pat. No.9,891,177 issued on Feb. 13, 2018, all of which are incorporated hereinin their entirety. Further, for the purposes of this disclosure, aparticle may include any surface defect on a sample of interestincluding, but not limited to, a foreign particulate, a scratch, a pit,a hole, a bump, or the like.

It is recognized herein that light scattered from a particle and lightscattered from a surface may exhibit different electric fielddistributions (e.g., polarization and electric field strength) as afunction of scattering angle. Further, differences in the electric fielddistribution (e.g., scattering map) may be particularly significant forobliquely-incident p-polarized light. For example, surface haze fromobliquely-incident p-polarized light may be approximately radiallypolarized with respect to an angle of specular reflection, whereasscattering from a particle may be approximately radially polarized withrespect to a surface normal.

In some embodiments, a dark-field imaging system includes a polarizationrotator in a pupil plane to selectively rotate the polarization ofsurface haze to a selected polarization angle and a linear polarizer toseparate the surface haze that is polarized along the selectedpolarization angle from the remaining signal (e.g., particle scattering)into different imaging channels. For example, the polarization rotatormay provide varying polarization rotation angles across the pupil planebased on a known or expected polarization distribution of surface haze,where a spatial distribution of polarization rotation angle across thepupil is selected to rotate the surface haze distributed across thepupil to a common selected polarization angle. In this regard, a linearpolarizer (e.g., a polarizing beamsplitter) aligned to this selectedpolarization angle may effectively separate the surface haze from theparticle scattering.

Additional embodiments of the present disclosure are directed to apolarization rotator for providing a spatially-varying amount ofpolarization rotation suitable for use in a pupil plane of an imagingsystem. Multiple configurations of a polarization rotator arecontemplated herein. In some embodiments, a polarization rotatorincludes a segmented half-wave plate including multiple half-wave plateswith different orientations of the optic axes. For example, thepolarization rotator may include multiple half-wave plates distributedradially around an apex location such as, but not limited to, a point inthe pupil plane corresponding to specular reflection of an illuminationbeam. In this regard, each half-wave plate may cover a range of radialangles around the specular reflection angle (e.g., to mimic theapproximately radial polarization distribution of surface haze). By wayof another example, the polarization rotator may include a series ofhalf-wave plates linearly distributed along a single direction in thepupil plane. In some embodiments, a polarization rotator includes anoptically-active material having a spatially-varying thickness. In thisregard, the thickness at a given point in the pupil plane may determinethe angle of polarization rotation.

Additional embodiments of the present disclosure are directed to amethod for designing a spatial distribution of polarization rotationangle suitable for rotating surface haze to a selected polarizationangle for filtering with a polarizing beamsplitter. For example, apolarization rotator may be designed to selectively rotate lightassociated with any source of noise to a common selected polarizationangle for filtering using a polarizing beamsplitter. Accordingly, whilethe present disclosure focuses primarily on surface haze based onobliquely-incident p-polarized light, the examples herein are providedsolely for illustrative purposes and should not be interpreted as alimitation. Rather, it is contemplated herein that the systems andmethods described herein may be applied to light with any wavelength,polarization, or angle of incidence.

Additional embodiments of the present disclosure are directed to asegmented polarizer suitable for use in a pupil plane of an imagingsystem for selectively filtering (e.g., through absorption in thesegmented polarizer) surface haze based on a known distribution ofpolarization angles of surface haze in the pupil plane. For example, asegmented polarizer may include multiple polarizers distributed acrossthe pupil plane, where each polarizer is oriented to block light along aselected direction. Multiple configurations of a segmented polarizer arecontemplated herein. In some embodiments, a segmented polarizer includesmultiple polarizers distributed radially around an apex location suchas, but not limited to, a point in the pupil plane corresponding tospecular reflection of an illumination beam. In some embodiments, asegmented polarizer includes multiple polarizers distributed linearly inthe pupil plane.

Referring now to FIGS. 1 through 13B, systems and methods for sensitiveparticle detection will be described in greater detail.

FIG. 1 is a conceptual view of a particle detection system 100, inaccordance with one or more embodiments of the present disclosure. Inone embodiment, the particle detection system 100 includes anillumination source 102 to generate an illumination beam 104, anillumination pathway 106 including one or more illumination optics todirect the illumination beam 104 to a sample 108, and a collectionpathway 110 including one or more collection optics to collect lightemanating from the sample 108 (e.g., sample light 112). For example, thecollection pathway 110 may include an objective lens 114 to collect atleast a portion of the sample light 112. The sample light 112 mayinclude any type of light emanating from the sample 108 in response tothe illumination beam 104 including, but not limited to, scatteredlight, reflected light, diffracted light, or luminescence.

The illumination beam 104 may include one or more selected wavelengthsof light including, but not limited to, ultraviolet (UV) radiation,visible radiation, or infrared (IR) radiation. For example, theillumination source 102 may provide, but is not required to provide, anillumination beam 104 having wavelengths shorter than approximately 350nm. By way of another example, the illumination beam 104 may providewavelengths of approximately 266 nm. By way of another example, theillumination beam 104 may provide wavelengths of approximately 213 nm.It is recognized herein that imaging resolution and light scattering bysmall particles (e.g., relative to the wavelength of the illuminationbeam 104) both generally scale with wavelength such that decreasing thewavelength of the illumination beam 104 may generally increase theimaging resolution and scattering signal from the small particles.Accordingly, illumination beam 104 may include short-wavelength lightincluding, but not limited to, extreme ultraviolet (EUV) light, deepultraviolet (DUV) light, or vacuum ultraviolet (VUV) light.

The illumination source 102 may include any type of light source knownin the art. Further, the illumination source 102 may provide anillumination beam 104 having any selected spatial or temporal coherencecharacteristics. In one embodiment, the illumination source 102 includesone or more laser sources such as, but not limited to, one or morenarrowband laser sources, one or more broadband laser sources, one ormore supercontinuum laser sources, or one or more white light lasersources. In another embodiment, the illumination source 102 includes alaser-driven light source (LDLS) such as, but not limited to, alaser-sustained plasma (LSP) source. For example, the illuminationsource 102 may include, but is not limited to, a LSP lamp, a LSP bulb,or a LSP chamber suitable for containing one or more elements that, whenexcited by a laser source into a plasma state, may emit broadbandillumination. In another embodiment, the illumination source 102includes a lamp source such as, but not limited to, an arc lamp, adischarge lamp, or an electrode-less lamp.

In another embodiment, the illumination source 102 provides a tunableillumination beam 104. For example, the illumination source 102 mayinclude a tunable source of illumination (e.g., one or more tunablelasers, and the like). By way of another example, the illuminationsource 102 may include a broadband illumination source coupled to anycombination of fixed or tunable filters.

The illumination source 102 may further provide an illumination beam 104having any temporal profile. For example, the illumination beam 104 mayhave a continuous temporal profile, a modulated temporal profile, apulsed temporal profile, and the like.

It is recognized herein that the strength of surface haze may depend onmultiple factors including, but not limited to incidence angle orpolarization of the illumination beam 104. For example, the strength ofsurface haze may be relatively high for near-normal angles of incidenceand may drop off for higher incidence angles. In one embodiment, theillumination pathway 106 may include one or more illumination opticssuch as, but not limited to, lenses 116, mirrors, and the like to directthe illumination beam 104 to the sample 108 at an oblique incidenceangle to decrease the generation of surface haze. The oblique incidenceangle may generally include any selected incidence angle. For example,the incidence angle may be, but is not required to be, greater than 60degrees with respect to a surface normal.

In another embodiment, the illumination pathway 106 includes one or moreillumination beam-conditioning components 118 suitable for modifyingand/or conditioning the illumination beam 104. For example, the one ormore illumination beam-conditioning components 118 may include, but arenot limited to, one or more polarizers, one or more waveplates, one ormore filters, one or more beamsplitters, one or more diffusers, one ormore homogenizers, one or more apodizers, or one or more beam shapers.In one embodiment, the one or more illumination beam-conditioningcomponents 118 include a polarizer or waveplate oriented to provide ap-polarized illumination beam 104 on the sample 108.

In another embodiment, the particle detection system 100 includes atleast one detector 120 configured to capture at least a portion of thesample light 112 collected by the collection pathway 110. The detector120 may include any type of optical detector known in the art suitablefor measuring illumination received from the sample 108. For example, adetector 120 may include a multi-pixel detector suitable for capturingan image of the sample 108 such as, but not limited to, a charge-coupleddevice (CCD) detector, a complementary metal-oxide-semiconductor (CMOS)detector, a time-delayed integration (TDI) detector, a photomultipliertube (PMT) array, an avalanche photodiode (APD) array, or the like. Inanother embodiment, a detector 120 includes a spectroscopic detectorsuitable for identifying wavelengths of the sample light 112.

The particle detection system 100 may include any number of detectors120 to simultaneously image the sample 108. Further, the collectionpathway 110 may include a linear polarizer 122 configured to filter thesample light 112 to be imaged on a detector 120 based on polarization.In one embodiment, as illustrated in FIG. 1, the linear polarizer 122operates as a polarizing beamsplitter such that linear polarizer 122splits the sample light 112 into two orthogonally-polarized beams. Theparticle detection system 100 may then include a detector 120 forgenerating an image of the sample 108 with each of theorthogonally-polarized portions the sample light 112.

The collection pathway 110 may include any number of beam-conditioningelements 124 to direct and/or modify the sample light 112 including, butnot limited to, one or more lenses, one or more filters, one or moreapertures, one or more polarizers, or one or more phase plates.

In one embodiment, as illustrated in FIG. 1, the collection pathway 110includes one or more beam-conditioning elements 124 located at or near apupil plane 126. For example, as will be discussed in greater detailbelow, the collection pathway 110 may include beam-conditioning elements124 such as, but not limited to, a continuous polarizer or a phase maskat or near a pupil plane 126. In this regard, the particle detectionsystem 100 may control and/or adjust selected aspects of the samplelight 112 used to generate an image on the detector 120 including, butnot limited to, the intensity, phase, and polarization of the samplelight 112 as a function of scattering angle and/or position on thesample.

Further, the collection pathway 110 may have any number of pupil planes126. For example, as illustrated in FIG. 1, the collection pathway 110may include one or more lenses 128 to generate an image of the pupilplane 126 and one or more lenses 130 to generate an image of the surfaceof the sample 108 on the detector 120. However, it is recognized hereinthat a limited number of beam-conditioning elements 124 may be placed ata particular pupil plane 126 or sufficiently near a particular pupilplane 126 to provide a desired effect. Accordingly, for the purposes ofthe present disclosure, reference to one or more elements at a pupilplane 126 may generally describe one or more elements at or sufficientlyclose to a pupil plane 126 to produce a desired effect. In someembodiments, though not shown, the collection pathway 110 may includeadditional lenses to generate one or more additional pupil planes 126such that any number of beam-conditioning elements 124 may be placed ator near a pupil plane 126.

In another embodiment, the particle detection system 100 includes acontroller 132 including one or more processors 134 configured toexecute program instructions maintained on a memory medium 136 (e.g.,memory). Further, the controller 132 may be communicatively coupled toany components of the particle detection system 100. In this regard, theone or more processors 134 of controller 132 may execute any of thevarious process steps described throughout the present disclosure. Forexample, the controller 132 may receive, analyze, and/or process datafrom the detector 120 (e.g., associated with an image of the sample108). By way of another example, the controller 132 may control orotherwise direct any components of the particle detection system 100using control signals.

The one or more processors 134 of a controller 132 may include anyprocessing element known in the art. In this sense, the one or moreprocessors 134 may include any microprocessor-type device configured toexecute algorithms and/or instructions. In one embodiment, the one ormore processors 134 may consist of a desktop computer, mainframecomputer system, workstation, image computer, parallel processor, or anyother computer system (e.g., networked computer) configured to execute aprogram configured to operate the particle detection system 100, asdescribed throughout the present disclosure. It is further recognizedthat the term “processor” may be broadly defined to encompass any devicehaving one or more processing elements, which execute programinstructions from a non-transitory memory medium 136. Further, the stepsdescribed throughout the present disclosure may be carried out by asingle controller 132 or, alternatively, multiple controllers.Additionally, the controller 132 may include one or more controllershoused in a common housing or within multiple housings. In this way, anycontroller or combination of controllers may be separately packaged as amodule suitable for integration into particle detection system 100.

The memory medium 136 may include any storage medium known in the artsuitable for storing program instructions executable by the associatedone or more processors 134. For example, the memory medium 136 mayinclude a non-transitory memory medium. By way of another example, thememory medium 136 may include, but is not limited to, a read-only memory(ROM), a random-access memory (RAM), a magnetic or optical memory device(e.g., disk), a magnetic tape, a solid-state drive, and the like. It isfurther noted that memory medium 136 may be housed in a commoncontroller housing with the one or more processors 134. In oneembodiment, the memory medium 136 may be located remotely with respectto the physical location of the one or more processors 134 andcontroller 132. For instance, the one or more processors 134 ofcontroller 132 may access a remote memory (e.g., server), accessiblethrough a network (e.g., internet, intranet, and the like). Therefore,the above description should not be interpreted as a limitation on thepresent invention but merely an illustration.

It is contemplated herein that the particle detection system 100 may beconfigured as any type of image-based particle detection system known inthe art. In one embodiment, as illustrated in FIG. 1, the particledetection system 100 is a dark-field imaging system to excludespecularly-reflected light. In this regard, the particle detectionsystem 100 may image the sample 108 based primarily on scattered light.Dark-field imaging may further be implemented using any technique knownin the art. In one embodiment, an orientation and/or a numericalaperture (NA) of the objective lens 114 may be selected such that theobjective lens 114 does not collect specularly-reflected light. Forexample, as illustrated in FIG. 1, the objective lens 114 is orientedapproximately normal to the sample 108 and has a NA that does notinclude a specularly-reflection portion of the illumination beam 104.Further, the objective lens 114 may have, but is not required to have, aNA of approximately 0.9 or greater. In another embodiment, the particledetection system 100 may include one or more components to blockspecular reflection from reaching the detector 120.

Referring now to FIGS. 2A through 3B, pupil-plane polarization rotationof surface haze and subsequent filtering is described in greater detail.

It is recognized herein that light scattered from the surface of asample (e.g., surface haze, surface scattering, or the like) may beconsidered noise in particle detection applications. Accordingly, it maybe desirable to filter portions of the sample light 112 associated withsurface haze from portions of the sample light 112 associated with lightscattered by particles of interest.

FIG. 2A is a pupil-plane scattering map 202 of surface scattering (e.g.,surface haze) in response to obliquely-incident p-polarized light, inaccordance with one or more embodiments of the present disclosure. FIG.2B is a pupil-plane scattering map 204 of light scattered by a smallparticle (e.g., small relative to an imaging resolution of the particledetection system 100 or a wavelength of the illumination beam 104) inresponse to obliquely-incident p-polarized light, in accordance with oneor more embodiments of the present disclosure.

In particular, the scattering maps 202, 204 include the electric fieldstrength indicated by the shading with white as the highest intensityand black as the lowest intensity. Further, the scattering maps 202, 204include the polarization orientation of light as a function ofcollection angle (e.g., scattering angle) in the pupil plane 126indicated by the overlaid ellipses. The scattering maps 202, 204 arebounded by a collection area 206 in the pupil plane 126, which isassociated with the range of angles that sample light 112 is collectedby the particle detection system 100. For example, the collection area206 may correspond to the numerical aperture (NA) of the objective lens114.

The scattering maps 202, 204 are based on a configuration of theparticle detection system 100 illustrated in FIG. 1. In FIGS. 2A and 2B,the specular reflection angle 208 is located outside of the collectionarea 206 along the illumination direction 210 (e.g., outside thecollection area 206 on the right side of the circular collection area206 in FIG. 2A), indicating that the objective lens 114 does not capturespecularly-reflected light. However, alternative configurations arewithin the scope of the present disclosure. For example, in the casethat the specular reflection angle 208 lies within the pupil plane 126,the specularly-reflected light may be blocked prior to the detector 120to generate a dark-field image.

Additionally, the scattering maps 202, 204 may be representative ofscattering from a wide variety of materials including, but not limitedto, silicon, epitaxial, and poly-silicon wafers. However, it is to beunderstood that the scattering maps 202, 204 are provided solely forillustrative purposes and should not be interpreted as limiting thepresent disclosure.

As illustrated in FIGS. 2A and 2B, the electric field distribution(e.g., electric field strength and polarization orientation) of lightscattered by a particle may differ substantially from the electric fielddistribution of light scattered by a surface, particularly when theillumination beam 104 is p-polarized. For example, sample light 112associated with surface haze generally exhibits an approximately radialpolarization distribution with respect to the specular reflection angle208 in the collection area 206 as illustrated in FIG. 2A. In contrast,sample light 112 associated with particle scattering generally exhibitsa radial polarization distribution with respect to the surface normal asillustrated in FIG. 2B. Further, the polarization of the scatteredsample light 112 is generally elliptical. As can be seen from FIGS. 2Aand 2B, at most locations in the pupil plane 126, the ellipses are veryelongated meaning that one linear polarization component is muchstronger than the other. For the sample light 112 scattered from a smallparticle (e.g., FIG. 2B), the polarization may be more elliptical nearthe center of the pupil, meaning that the two linear polarizationcomponents can be roughly comparable in magnitude. However, theintensity of the light in this region of the pupil is relatively low andcontribute little to the total scattering signal from a small particle.

In one embodiment, the particle detection system 100 includes apolarizer located at or near the pupil plane 126 to preferentiallyreject surface haze. In a general sense, a polarizer located at or nearthe pupil plane 126 may be designed to provide spatially-varyingpolarization-filtering corresponding to any known, measured, simulated,or otherwise expected polarization of light. In the context of thepresent disclosure, a polarizer located at or near the pupil plane 126may preferentially filter surface haze based on a known electric fielddistribution in the pupil plane 126. Accordingly, in some embodiments,the particle detection system 100 includes a radial haze-rejectionpolarizer located at or near the pupil plane 126 to preferentiallyreject the approximately radially-polarized surface haze illustrated inFIG. 2A.

Referring now to FIGS. 3A and 3B, a segmented haze-rejection polarizer302 suitable for preferentially filtering surface haze from particlescattering are described in accordance with one or more embodiments ofthe present disclosure. In a general sense, a haze-rejection polarizer302 may be designed to provide spatially-varying polarization-filteringcorresponding to any known, measured, simulated, or otherwise expectedpolarization of light. In the context of the present disclosure, ahaze-rejection polarizer 302 may preferentially filter surface hazebased on a known electric field distribution in the pupil plane 126(e.g., the electric field distribution of surface haze illustrated inFIG. 2A). FIGS. 3A and 3B include polarization ellipses 304representative of the polarization of surface haze in the pupil plane126 based on FIG. 2A.

A haze-rejection polarizer 302 may include any number of segments 306distributed across the pupil plane 126, where each segment 306 mayinclude a linear polarizer oriented pass light polarized along aselected pass polarization direction 308. In this regard, thehaze-rejection polarizer 302 may provide a spatially-varyingdistribution of passed polarization angles.

In one embodiment, the pass polarization direction 308 of each segment306 of a haze-rejection polarizer 302 is oriented to preferentiallyreject surface haze. For example, the pass polarization direction 308for each segment 306 may be oriented orthogonal to the expectedpolarization ellipses 304 within the corresponding portion of the pupilplane 126.

FIG. 3A is a conceptual top view of a haze-rejection polarizer 302(e.g., an angularly-segmented polarizer) having wedge-shaped segments306 distributed radially around an apex location 310, in accordance withone or more embodiments of the present disclosure. In one embodiment,the apex location 310 of the haze-rejection polarizer 302 is oriented tocoincide with a point in the pupil plane 126 associated with specularreflection angle of the illumination beam 104 from the sample 108. Inthis regard, each segment 306 may cover a range of radial angles in thepupil plane 126 with respect to the specular reflection angle 208 suchthat surface haze within each segment 306 may be substantially uniformbased on the scattering map 202 in FIG. 2A. Further, each the passpolarization direction 308 for each segment 306 may be oriented toreject light having a radial polarization with respect to the apexlocation 310 in order to preferentially reject the surface haze.

The specular reflection angle 208 may be located within or outside ofthe collection area 206 as described previously herein. Further, apexlocation 310 need not necessarily lie within the physical structure ofthe haze-rejection polarizer 302. For example, in the case where thespecular reflection angle 208 is located outside of the collection area206, the segments 306 may be oriented as if they would converge on anapex location 310 outside the boundaries defining the size of thehaze-rejection polarizer 302.

FIG. 3B is a conceptual top view of a haze-rejection polarizer 302(e.g., a linearly-segmented polarizer) in which segments 306 arelinearly distributed along a selected segmentation direction 312 in thepupil plane 126, in accordance with one or more embodiments of thepresent disclosure. For example, the segmentation direction 312 in FIG.3B is selected to be orthogonal to the illumination direction 210 asrepresented in the pupil plane 126. In this regard, the passpolarization direction 308 for each segment 306 may be chosen tosubstantially reduce the transmission of the surface scattered lightthrough that segment 306.

It is recognized herein that the accuracy at which the haze-rejectionpolarizer 302 may preferentially filter surface haze may vary based onthe number and layout of segments 306 with respect to an expectedscattering map of surface haze. It is further recognized herein that themanufacturing cost of a haze-rejection polarizer 302 may also scale withcomplexity. Accordingly, the number and layout of segments 306 may beselected to balance various requirements including performance,manufacturing cost, and the like.

Further, the in the case that the polarization ellipses 304 are notuniformly oriented in a particular segment 306, the pass polarizationdirection 308 in a particular segment 306 may be selected to rejectsurface haze according to an optimization function. For example, thepass polarization direction 308 for each segment 306 may be selectedbased on an expected polarization distribution (e.g., as illustrated inFIG. 2A, or the like) to be orthogonal to a weighted average of theexpected directions of the long axes of the polarization ellipses 304within each segment 306, where the weighting is proportional to theexpected field strength or intensity across the segment 306. By way ofanother example, the pass polarization direction 308 for each segment306 may be selected to maximize the ratio of transmitted sample light112 associated with particle scattering to transmitted surface haze.

Referring now to FIG. 4, in some embodiments, the particle detectionsystem 100 includes one or more components located at or near the pupilplane 126 to reshape the point spread function (PSF) of p-polarizedlight scattered by sub-resolution particles. It is recognized hereinthat the image of a particle smaller than an imaging resolution of asystem is generally limited by the system PSF, which is typically anAiry function when the image is formed from specularly-reflected light.However, the actual PSF associated with a particle (e.g., a particlePSF) and thus an actual image of the particle generated by a system isrelated to the particular electric field distribution of light from aparticle in the pupil plane 126 and may have a different size or shapethan the system PSF, particularly when the image is formed fromscattered light.

In particular, a dark-field image of a particle (e.g., an image of aparticle formed with scattered or diffracted light) smaller than theimaging resolution when illuminated with oblique p-polarized light maybe an annulus that spreads to an area larger than the system PSF, whichnegatively impacts particle detection sensitivity. This annulus shapeand increase in the size of the PSF or imaged spot of a particle may beassociated with destructive interference of collected light at a centerof the imaged spot of a particle on the detector 120.

Accordingly, in some embodiments, the particle detection system 100includes one or more components to modify the phase of sample light 112across the pupil plane 126 to facilitate constructive interference oflight at the center of an imaged spot of a particle on the detector 120such as, but not limited to, one or more phase plates or one or morephase compensators.

For example, a phase mask may have various configurations suitable forreshaping the PSF of imaged particles. Phase masks for reshaping the PSFof imaged particles based on scattered light are generally described inU.S. patent application Ser. No. 16/577,089 titled RADIAL POLARIZER FORPARTICLE DETECTION and filed on Sep. 20, 2019, which is incorporatedherein by reference in its entirety. In some embodiments, a phase maskmay include one or more half-wave plates covering selected portions ofthe pupil plane 126. In this regard, the phase mask may be formed as asegmented optic where at least one of the segments includes a half-waveplate.

FIG. 4 is a conceptual top view of a phase mask 402 including twosegments to divide the pupil into two segments (e.g., halves), inaccordance with one or more embodiments of the present disclosure. Forexample, as illustrated in FIG. 4, the phase mask 402 may include asegment 404 formed from a half-wave plate with an optic axis along an Xdirection to introduce a phase shift of π for light polarized along theY direction with respect to orthogonal polarizations (represented ase^(iπ)E_(y)). Further, the phase mask 402 may include a segment 406 thatdoes not rotate the polarization of light. For example, the segment 406may include a compensating plate formed from an optically homogenousmaterial along the direction of propagation such that light through thesegment 406 propagates along the same (or substantially the same)optical path length as light in segment 404. In one embodiment, thecompensating plate is formed from a material having approximately thesame thickness and index of refraction as a half-wave plate in segment404, but without birefringence along the propagation direction. Inanother embodiment, the compensating plate is formed from the samematerial as the half-wave plate in segment 404, but cut along adifferent axis such that light propagating through the compensatingplate does not experience birefringence. For instance, light propagatingalong the optic axis of a uniaxial crystal may not experiencebirefringence such that the crystal may be optically homogenous forlight propagating along the optic axis. By way of another example, thesegment 406 may include an aperture.

Further, in some embodiments, a phase mask 402 may be tilted out of thepupil plane 126 to at least partially compensate for optical path lengthdifferences across the pupil plane 126.

A segmented phase mask 402 may be formed using any technique known inthe art. In one embodiment, the various segments (e.g., segments 404-406of FIG. 4) are formed as a single component in which the varioussegments are placed in a single plane.

It is to be understood, however, that FIG. 4 and the associateddescription are provided solely for illustrative purposes and should notbe interpreted as limiting. For example, a phase mask 402 with twosegments may include a half-wave plate placed in the bottom portion ofthe collection area 206 rather than the top portion as illustrated inFIG. 4. Further, the phase mask 402 may include any number of segmentsdistributed formed from any combination of materials in any patternacross the pupil plane 126 so as to reshape the PSF of light scatteredfrom a particle. For example, given a known electric field distributionof light in the pupil plane 126 (e.g., measured, simulated, or the like)associated with an object of interest, a segmented phase mask 402 asdescribed herein may be formed to selectively adjust the phase ofvarious regions of light in the pupil plane 126 to reshape the PSF of animage of the object of interest. In particular, the various segments ofthe phase mask 402 may be selected to facilitate constructiveinterference at a detector 120 to provide a tight PSF that approachesthe system PSF (e.g., within a selected tolerance).

It is further recognized herein that the design of the phase mask 402may represent a tradeoff between an “ideal” phase mask based on a knownelectric field distribution associated with particles of interest (e.g.,as illustrated in FIG. 2A, or the like) and practical design and/ormanufacturing considerations. For example, it may be the case that anideal or otherwise desired phase mask 402 is unjustifiably expensive ordifficult to manufacture. However, it may be the case that certaindesigns of the phase mask 402 may satisfy both manufacturing andperformance specifications (e.g., a particle PSF having a selectedshape, or the like). Accordingly, the designs of the phase mask 402illustrated in FIG. 4 may represent a non-limiting example providing aparticular tradeoff between performance and manufacturability.

In another embodiment, as will be described in greater detail below, theparticle detection system 100 may include a phase compensator formedfrom an optical homogenous material having a spatially-varying thicknessacross the pupil plane 126 to facilitate constructive interference ofsample light 112 associated with particle scattering at a center of animage of the particle on the detector 120.

As described previously herein, it is contemplated herein that variouscombinations of optical components may be used to selectively filtersurface haze from sample light 112 scattered by a particle on a sample108. Referring now to FIGS. 5 through 14B, in some embodiments, aparticle detection system 100 includes a polarization rotator 502 torotate surface haze across the pupil plane 126 to a selected commonpolarization angle followed by a linear polarizer 122 oriented to rejectlight along the selected polarization direction. For example, apolarization rotator 502 in the pupil plane 126 may provide aspatially-varying amount of polarization rotation (e.g., aspatially-varying polarization rotation angle) across the pupil plane126. This spatial distribution of the polarization rotation angle may beselected based on an expected electric field distribution of surfacehaze (e.g., the scattering map 202 in FIG. 2A) to selectively rotate thepolarization of surface haze across the pupil plane 126 to the selectedpolarization angle. The particle detection system 100 may additionallyinclude a linear polarizer (e.g., the linear polarizer 122) aligned toreject light polarized along the selected polarization angle.

Further, it is contemplated herein that the selected polarization anglefor rejection of the surface haze may be any suitable angle. Forexample, the selected polarization angle may be chosen based on anexpected distribution of particle-scattered sample light 112 (e.g., asillustrated in FIG. 2B) to minimize the intensity of rejectedparticle-scattered sample light 112.

The linear polarizer 122 may reject the sample light 112 polarized alongthe selected polarization direction via any process includingtransmission, reflection, or absorption. In one embodiment, asillustrated in FIG. 1, the linear polarizer 122 includes a polarizingbeamsplitter such that the sample light 112 polarized along the selectedpolarization direction (primarily surface haze) is directed along oneoptical path (e.g., via transmission or reflection) andorthogonally-polarized sample light 112 (primarily particle-scatteredsample light 112) is directed along another optical path. Accordingly,the particle detection system 100 may include a detector 120 in eitheror both optical paths to generate images of the sample 108 based on thecorresponding portion of the sample light 112.

It is recognized herein that retaining the portion of the sample light112 associated with surface haze may be desirable in many applications.For example, it may be desirable to monitor relative signal strengthsassociated with surface haze and particle scattering. By way of anotherexample, it may be desirable to generate an image associated withsurface haze. In some instances, a sample imaged with surface haze mayprovide additional relevant metrology data associated with the samplesurface. Further, it may be the case that the combination of thepolarization rotator 502 and linear polarizer 122 may not fully separatethe surface haze from the particle-scattered sample light 112.Accordingly, a multi-channel imaging system in which a first channelprimarily includes light scattered from particles and a second channelprimarily includes light scattered from the surface may facilitateverification of the system performance suitable for refining the designof the polarization rotator 502.

The polarization rotator 502 may be formed from a variety of opticalcomponents. In some embodiments, as illustrated in FIGS. 5 through 8B, apolarization rotator 502 is formed from a segmented half-wave plate. Inthis regard, the polarization rotator 502 may include two or morehalf-wave plates distributed across the pupil plane 126, each having anoptic axis oriented in a selected direction to provide a selectedspatial distribution of polarization rotation angles. In someembodiments, as illustrated in FIGS. 12 through 14B, a polarizationrotator 502 includes an optically-active material having aspatially-varying thickness to provide a selected spatial distributionof polarization rotation angles. However, it is to be understood thatthe examples provided herein are merely illustrative and should not beinterpreted as limiting.

Referring now to FIGS. 5 through 8B, a polarization rotator 502 formedfrom a segmented half-wave plate is described in accordance with one ormore embodiments of the present disclosure.

In one embodiment, a polarization rotator 502 includes multiple segments504 distributed throughout the pupil plane 126, where each segment 504of the polarization rotator 502 includes a half-wave plate formed from auniaxial crystal cut with an optic axis 506 oriented perpendicular tothe propagation direction through the crystal and a thickness selectedto provide a π-phase shift between orthogonal polarizations, which mayhave the effect of rotating the polarization of light. In particular,light polarized with an angle θ with respect to the optic axis 506 maybe rotated by 2θ. In another embodiment, the optic axis 506 of thehalf-wave plate in each segment 504 is oriented to rotate thepolarization of surface haze within the segment 504 to the selectedpolarization angle.

FIGS. 5 through 6B illustrate a polarization rotator 502 formed as anangularly-segmented half-wave plate in accordance with one or moreembodiments of the present disclosure.

FIG. 5 is a conceptual top view of a polarization rotator 502 formed asan angularly-segmented half-wave plate, in accordance with one or moreembodiments of the present disclosure. For example, theangularly-segmented half-wave plate illustrated in FIG. 5 may be similarto the haze-rejection polarizer 302 illustrated in FIG. 3A includinghalf-wave plates instead of polarizers.

In one embodiment, the polarization rotator 502 includes wedge-shapedsegments 504 distributed radially around an apex location 508. Inanother embodiment, the apex location 508 corresponds to the specularreflection angle of the illumination beam 104 from the sample 108, whichmay be located within or outside of the collection area 206. In thisregard, each segment 504 may cover a range of radial angles in the pupilplane 126 with respect to the specular reflection angle 208 such thatsurface haze within each segment 504 may be substantially uniform basedon the scattering map 202 in FIG. 2A.

FIGS. 6A and 6B are plots 602, 604 of orthogonally polarized portions ofthe collected sample light 112 after propagating through anangularly-segmented polarization rotator 502 (e.g., illustrated in FIG.4) and a polarizing linear polarizer 122, in accordance with one or moreembodiments of the present disclosure. For example, plot 602 mayprimarily include surface haze and plot 604 may primarily includeparticle scattering.

FIG. 7A is a conceptual top view of a polarization rotator 502 formed asa linearly-segmented half-wave plate, in accordance with one or moreembodiments of the present disclosure. For example, thelinearly-segmented half-wave plate illustrated in FIG. 7A may be similarto the haze-rejection polarizer 302 illustrated in FIG. 3B includinghalf-wave plates instead of polarizers.

In one embodiment, the polarization rotator 502 includes segments 504distributed linearly along a segmentation direction 702. For example,the segmentation direction 702 in FIG. 7A is selected to be orthogonalto the illumination direction 210 as represented in the pupil plane 126.However, it is to be understood that a polarization rotator 502 may bedesigned to have the segmentation direction 702 along any direction inthe pupil plane 126.

FIG. 7B is a calculated plot 704 of orientation directions for opticaxes 506 of the linearly-segmented polarization rotator 502 shown inFIG. 7A as a function of position in the pupil plane 126 along thesegmentation direction 702, in accordance with one or more embodimentsof the present disclosure. In particular, FIG. 7B illustratesorientations of the optic axes 506 relative to the illuminationdirection 210 of the illumination beam 104 for wavelengths of 266 nm and213 nm, respectively. Further, the plot 704 is calculated for aconfiguration of the particle detection system 100 including a phasemask (e.g., the phase mask 402, or the like) at or near the pupil plane126 prior to the polarization rotator 502 to reshape the PSF of theparticle-scattered light to provide constructive interference at acentral portion of an imaged particle.

For example, a linearly-segmented polarization rotator 502 may bedesigned to include a selected number of segments 504, each occupying arange of positions along the X-axis of the plot 704. Further, theorientation angle of the optic axis 506 in each segment 504 may beselected based on the plot 704 using any selection technique known inthe art. For instance, the orientation angle of the optic axis 506 ineach segment 504 may be selected as the midpoint, average, or any otherselection metric of the corresponding range of angles in the respectiveposition in the pupil plane 126.

It is to be understood, however, that the illustrations of thepolarization rotator 502 in FIGS. 7A and 7B are provided solely forillustrative purposes and should not be interpreted as limiting. Rather,the polarization rotator 502 may include any number and size of segments504 having any selected orientation of optic axes 506 to rotate thepolarization of surface haze to a selected polarization angle forrejection using the linear polarizer 122. FIG. 7C is a plot 706 oforientation directions for optic axes 506 of a linearly-segmentedpolarization rotator 502 to rotate the polarization of surface haze to aselected polarization angle, in accordance with one or more embodimentsof the present disclosure.

FIGS. 8A and 8B are plots 802, 804 of orthogonally polarized portions ofthe collected sample light 112 after propagating through anangularly-segmented polarization rotator 502 (e.g., illustrated in FIG.5) and a linear polarizer 122, in accordance with one or moreembodiments of the present disclosure. In this regard, plot 802 mayinclude primarily surface haze and plot 804 may include primarilyparticle scattering.

As described previously herein with respect to the haze-rejectionpolarizer 302, it is recognized herein that the accuracy at which theoptic axes 506 may map to preferentially align the polarization ofsurface haze across the pupil plane 126 to the selected polarizationangle based on an expected electric field distribution (e.g., scatteringmap 202 of FIG. 2A) may vary based on the number and layout of segments504. It is further recognized herein that the manufacturing cost of apolarization rotator 502 may also scale with complexity. Accordingly,the number and layout of segments 504 may be selected to balance variousrequirements including performance, manufacturing cost, and the like.

Further, in the case that the polarization ellipses 304 are notuniformly oriented in a particular segment 504, the orientation of theoptic axis 506 in each segment 504 may be selected to enable rejectionof surface haze according to an optimization function. For example, theoptic axis 506 for each segment 504 may be selected to maximize thepower of surface haze rotated to a selected polarization by the segmentbased on the expected distribution of intensity and/or polarizationwithin the segment 504 (e.g., within a selected tolerance). By way ofanother example, the orientation of the optic axis 506 for each segment504 may be selected to balance the power of particle scattering passedby a polarizer placed downstream of the polarization rotator 502 (e.g.,linear polarizer 122) with the power of the surface haze rejected by thepolarizer.

Referring now to FIGS. 9A through 9C, the use of a phase mask to reshapea point spread function (PSF) associated with images of particlessmaller than an imaging resolution will be described in greater detailin accordance with one or more embodiments of the present disclosure. Inparticular, FIGS. 9B and 9C were generated using the phase mask 402configured as illustrated in FIG. 4 located at or near the pupil plane126 prior to the respective polarization rotator 502.

FIG. 9A is an image 902 of a particle smaller than a resolution of animaging system (e.g., the particle detection system 100) generated basedon scattering of obliquely-incident p-polarized light, in accordancewith one or more embodiments of the present disclosure. As illustratedby FIG. 9A, the PSF of a particle based on p-polarized scattered lightis annular-shaped rather than an Airy function, which is at least partlya result of the interference pattern associated with the particularpolarization distribution of light in the pupil plane 126 and the use ofscattered light to form the image 902. In particular, destructiveinterference associated with a central point 904 in FIG. 9A results indecreased intensity at the central point 904 in the image 902 and aradial shifting of the intensity outward from the central point 904. Asa result, the signal strength and thus the signal to noise ratioassociated with an image of a particle is negatively impacted.

FIG. 9B includes an image 906 of the particle in FIG. 9A using animaging system (e.g., the particle detection system 100) with anangularly-segmented polarization rotator 502 as illustrated in FIG. 5and a linear polarizer 122, in accordance with one or more embodimentsof the present disclosure. In particular, the angularly-segmentedpolarization rotator 502 includes segments 504 having an angular widthof 5°. FIG. 9C includes an image 908 of the particle in FIG. 9A using animaging system (e.g., the particle detection system 100) with alinearly-segmented polarization rotator 502 as illustrated in FIG. 7Awith 72 segments 504 and a linear polarizer 122, in accordance with oneor more embodiments of the present disclosure. As illustrated in FIGS.9A through 9C, the image of a particle generated without a phase mask asdescribed herein has an annular shape with an intensity dip in thecentral point 904. However, incorporating the phase mask tightens thePSF such that an image of a particle has a central peak and a tighterdistribution of intensity around the central point 904.

FIG. 10 is a plot 1002 illustrating the performance and convergencebehavior of an angularly-segmented polarization rotator 502 and alinearly-segmented polarization rotator 502, in accordance with one ormore embodiments of the present disclosure. In particular, FIG. 10illustrates the signal to noise ratio (SNR) of sample light 112associated with an image of a particle with respect to background noiseincluding, but not limited to, surface haze.

In particular, FIG. 10 corresponds to an image generated with lightshown in FIG. 8B, where the illumination beam 104 is p-polarized andincident on a bare silicon wafer at an angle of 70° and the objectivelens 114 has a NA of 0.97. The SNR in FIG. 10 is defined by thefollowing formula:

$\begin{matrix}{{SNR} = \frac{signal}{\sqrt[3]{\sigma_{wafer} + \sigma_{laser} + \sigma_{shot} + \sigma_{detector}}}} & (1)\end{matrix}$

where signal is the peak signal strength associated with an image of aparticle (e.g., the signal strength of the central point 904 in the casea phase plate is used to reshape the PSF), σ_(wafer) is the waferbackground noise, σ_(laser) is the laser noise, σ_(shot) is the shotnoise, and σ_(detector) is the readout noise of the detector 120. Asshown in FIG. 10, increasing the number of segments 504 generallyincreases the particle detection SNR, where the SNR reaches anasymptotic limit with increasing segments 504.

Referring now to FIGS. 11A and 11B, the performance of variousconfigurations of a haze-rejection polarizer 302 and a segmentedpolarization rotator 502 are compared. FIG. 11A is a plot 1102 of SNR asa function of pixel size (e.g., of the detector 120) for variousconfigurations of a haze-rejection polarizer 302 and a segmentedpolarization rotator 502 using an illumination beam 104 with awavelength of 266 nm, in accordance with one or more embodiments of thepresent disclosure. FIG. 11B is a plot 1104 of SNR as a function ofpixel size (e.g., of the detector 120) for various configurations of ahaze-rejection polarizer 302 and a segmented polarization rotator 502using an illumination beam 104 with a wavelength of 213 nm, inaccordance with one or more embodiments of the present disclosure.

In particular, FIGS. 11A and 11B illustrate the SNR 1106 of anangularly-haze-rejection polarizer 302 (e.g., as illustrated in FIG.3A), SNR 1108 of a linearly-haze-rejection polarizer 302 (e.g., asillustrated in FIG. 3B), SNR 1110 of an angularly-segmented polarizationrotator 502 (e.g., as illustrated in FIG. 4) plus a polarizing linearpolarizer 122, and a SNR 1112 of a linearly-segmented polarizationrotator 502 (e.g., as illustrated in FIG. 6) plus a polarizing linearpolarizer 122. Further, the signals in FIGS. 10A and 10B are based onparticle detection system 100 incorporating a phase plate to reshape thePSF of a p-polarized illumination beam 104 by particles as describedpreviously herein.

In FIGS. 11A and 11B, similar performance may be achieved withangularly-segmented elements or linearly-segmented elements. Forexample, the SNR 1106 of the angularly-haze-rejection polarizer 302 iscomparable to the SNR 1110 of the angularly-segmented polarizationrotator 502 plus a polarizing linear polarizer 122. Similarly, the SNR1108 of the linearly-haze-rejection polarizer 302 is comparable to theSNR 1112 of the linearly-segmented polarization rotator 502 plus apolarizing linear polarizer 122.

It is noted that in FIGS. 10 through 11B, the linearly-segmentedelements (e.g., the linearly haze-rejection polarizer 302 andpolarization rotator 502) outperforms the angularly haze-rejectionpolarizer 302 elements (e.g., the angularly-segmented haze-rejectionpolarizer 302 and polarization rotator 502), though it is to beunderstood that this particular result should not be interpreted aslimiting. In a general sense, the performance of a particularpolarization rotator 502 may depend on a wide range of factorsincluding, but not limited to, the number and layout of segments 504,the specific orientations of the corresponding optic axes 506, themanufacturing precision, the material and surface roughness of thesample 108, the power of the illumination beam 104, and the noise of thedetector 120.

Referring now to FIGS. 12 through 14B, a polarization rotator 502 formedfrom an optically-active material having a varying thickness isdescribed in greater detail.

FIG. 12 is a conceptual top view of a polarization rotator 502 formedfrom an optically-active material, in accordance with one or moreembodiments of the present disclosure. In one embodiment, thepolarization rotator 502 is formed from an optically active materialsuch as, but not limited to, quartz. The amount by which an opticallyactive material rotates the polarization of light propagating through itdepends on the thickness of the material. Accordingly, a thickness ofthe polarization rotator 502 along the propagation direction (e.g., adirection normal to the plane of FIG. 12) may vary based on location inthe pupil plane 126. In this regard, light propagating through thepolarization rotator 502 may exhibit a different amount of polarizationrotation depending on the location of the light in the pupil plane 126(e.g., depending on the scattering angle).

In another embodiment, a spatial distribution of the polarizationrotation across the pupil plane 126 may be selected to preferentiallyrotate the polarization of surface haze to a selected polarization angle1202. Accordingly, a linear polarizer 122 may separate the surface hazepolarized along this selected polarization angle from the remaininglight (e.g., the particle scattering), at least within a selectedtolerance. For example, in FIG. 11, the polarization ellipses 304 ofsurface haze from the sample 108 prior to the polarization rotator 502(open ellipses) are oriented radially with respect to the specularreflection angle 208, while the polarization ellipses 1204 of thesurface haze after propagating through the polarization rotator 502(closed ellipses) are aligned along the selected polarization angle 1202(e.g., the X direction).

Referring now to FIGS. 13A through 14B, various designs of apolarization rotator 502 formed from an optically active material aredescribed in accordance with one or more embodiments of the presentdisclosure.

It is recognized herein that the accuracy at which an optically activepolarization rotator 502 may preferentially rotate the polarization ofsurface haze to the selected polarization angle 1202 may depend on howwell the spatial distribution of the polarization rotation angle acrossthe pupil plane 126 maps to the polarization distribution of surfacehaze at the pupil plane 126. It is contemplated herein that thepolarization rotator 502 may provide any spatial distribution of thepolarization rotation angles across the pupil plane 126. It is furthercontemplated herein that the manufacturing cost of the polarizationrotator 502 may also scale with complexity. Accordingly, the spatialdistribution of polarization rotation angles (e.g., the spatialdistribution of thickness) may be selected to balance variousrequirements including performance, manufacturing cost, and the like.

In one embodiment, the polarization rotator 502 includes atwo-dimensional spatial distribution of polarization rotation anglesacross the pupil plane 126. In another embodiment, the polarizationrotator 502 includes a one-dimensional spatial distribution ofpolarization rotation angles across the pupil plane 126. In this regard,the polarization rotation angle may vary along a single selecteddirection in the pupil plane 126 (e.g., the Y direction of FIGS. 12through 14B).

FIG. 13A is a plot 1302 of a thickness profile along the verticaldirection of FIG. 12 (e.g., the Y direction) of a polarization rotator502 formed from an optically active material designed to rotate thepolarization of surface haze having wavelengths of 266 nm and 213 nm,respectively, to the horizontal direction in FIG. 12 (e.g., the Xdirection), in accordance with one or more embodiments of the presentdisclosure. In particular, FIG. 13A illustrates a symmetric design ofthe polarization rotator 502 about the Z axis (e.g., with respect to aposition of 0 in FIG. 13A), which is intended to be used with a phasemask (e.g., phase mask 402 illustrated in FIG. 4) at or near the pupilplane 126 and prior to the polarization rotator 502 to reverse thephases of the Y polarizations in one half of the pupil plane before thelight arrives at polarization rotator 502.

The thickness in FIG. 13A is provided in units of micrometers [(μm)/Δn],where Δn represents a difference between refractive index experienced bylight having opposite circular polarizations through the polarizationrotator 502. Further, the zero thickness represents a referencethickness according to mλ/Δn, where λ is the wavelength of theillumination beam 104 and m is an arbitrary positive integer.

FIG. 13B is a cross-sectional view 1304 of a polarization rotator 502having a thickness profile along a propagation direction (e.g., the Zdirection) based on FIG. 13A, in accordance with one or more embodimentsof the present disclosure. It is recognized herein that the thicknessprofile in FIG. 13A includes a sharp thickness transition around acentral point 1306 that may be difficult to manufacture with anoptically-polished surface. Accordingly, the cross-sectional view inFIG. 13B represents a deviation from the thickness profile of FIG. 13Ato improve manufacturability.

In another embodiment, the particle detection system 100 includes acompensator 1308 to correct the optical path lengths of different raysso that they are approximately equal (e.g., equal across the pupil plane126 within a selected tolerance such as, but not limited to, a phasedifference of π/2). For example, the compensator 1308 may be formed froman optically-homogenous material along the propagation direction (e.g.,the Z direction in FIG. 12). By way of another example, the compensator1308 may be formed from an optically active material that has theopposite handedness to the optically active material comprising thepolarization rotator 502. In one instance, the polarization rotator 502may comprise right-handed quartz and compensator 1308 may compriseleft-handed quartz, where each has a thickness profile selected suchthat the desired polarization rotations and phase corrections areachieved. In particular, the compensator 1308 may facilitateconstructive interference of light across the pupil plane 126 whenimaged on the detector 120. In this regard, the compensator 1308 mayfunction in a similar way as the phase mask 402 described previouslyherein by making the path length in one half of the Y planeapproximately π different from that in the other half. In oneembodiment, the compensator 1308 is formed from a material having asimilar refractive index to the optically active material forming thepolarization rotator 502. For example, the polarization rotator 502 maybe formed from crystalline quartz oriented with its optical axis in theZ direction and the compensator 1308 may be formed from fused silica.

FIG. 14A is a plot 1402 of a thickness profile along the verticaldirection of FIG. 12 (e.g., the Y direction) of a polarization rotator502 formed from an optically active material designed to rotate thepolarization of surface haze having wavelengths of 266 nm and 213 nm,respectively, to the horizontal direction in FIG. 12 (e.g., the Xdirection), in accordance with one or more embodiments of the presentdisclosure. Like FIG. 13A, the thickness in FIG. 14A is provided inunits of micrometers [(μm)/Δn] and the zero thickness represents areference thickness according to mλ/Δn. Further, the thickness profileof FIG. 14A does not include a sharp thickness transition as seen in thethickness profile of FIG. 13A.

[moo] FIG. 14B is a cross-sectional view 1404 of a polarization rotator502 having a thickness profile along a propagation direction (e.g., theZ direction) based on FIG. 14A and including a compensator 1308 tocorrect the optical path lengths of different rays so that they areapproximately equal (e.g., equal across the pupil plane 126), inaccordance with one or more embodiments of the present disclosure.

In another embodiment, the particle detection system 100 may include aphase mask (e.g., the phase mask 402 illustrated in FIG. 4, or the like)prior to both a polarization rotator 502 and a compensator 1308 (e.g.,as illustrated in FIGS. 13B and 14B) to further reshape the PSF ofimages of particles generated with scattered light by facilitatingconstructive interference at a central portion of the particle image onthe detector 120. It is further contemplated herein that some designs ofan optically-active polarization rotator 502 operate to provideconstructive interference of light across the pupil plane 126 whenimaged on the detector 120 such that a compensator 1308 is not necessaryto provide a desired PSF for particle scattering.

FIG. 15 is a flow diagram illustrating steps performed in a method 1500for particle detection, in accordance with one or more embodiments ofthe present disclosure. Applicant notes that the embodiments andenabling technologies described previously herein in the context of theparticle detection system 100 should be interpreted to extend to method1500. It is further noted, however, that the method 1500 is not limitedto the architecture of the particle detection system 100.

In one embodiment, the method 1500 includes a step 1502 of receiving afirst electric field distribution of light scattered from a surface of asample (e.g., surface haze) in response to an illumination beam with aknown polarization at a known incidence angle. In another embodiment,the method 1500 includes a step 1504 of receiving a second electricfield distribution of light scattered from a particle on the surface ofthe sample in response to the illumination beam.

In another embodiment, the method 1500 includes a step 1506 of designinga polarization rotator suitable for placement at a pupil plane of animaging system to rotate a polarization of light having the firstelectric field distribution to a selected polarization angle. Forexample, a polarization rotation angle of light passing through thepolarization rotator may be selected to vary across the pupil planeaccording to a spatial distribution that is selected to rotate thepolarization of light having the first electric field distribution tothe selected polarization angle.

For example, it may be the case that surface haze may have a differentelectric field distribution in a pupil plane of an imaging system thanlight scattered by particles on the surface. In particular, it isrecognized herein that surface haze and particle scattering havesubstantially different electric field distributions when scattered byobliquely-incident p-polarized light.

It is contemplated herein that a polarization rotator designed in step1506 may be formed from a variety of materials. In one embodiment, thepolarization rotator includes a segmented half-wave plate formed frommultiple half-wave plates distributed across the pupil plane havingoptic axes selectively oriented to rotate surface haze in the respectiveportions of the pupil plane to the first polarization angle. In anotherembodiment, the polarization rotator includes an optically activematerial such as, but not limited to, quartz having a spatially-varyingthickness profile. For example, polarization rotation of light in anoptically active material depends on the thickness of the opticallyactive material. Accordingly, a polarization rotator having aspatially-varying thickness profile may provide different polarizationrotation angles for light across the pupil plane.

In another embodiment, the method 1500 includes a step 1508 ofgenerating a dark-field image of a sample with the imaging system havingthe polarization rotator in the pupil plane and a polarizer aligned toreject light polarized along the selected polarization angle, where thedark-field image is based on light passed by the polarizer. For example,the light passed by the polarizer may correspond to light scattered byone or more particles on the surface of the sample within a selectedtolerance.

The herein described subject matter sometimes illustrates differentcomponents contained within, or connected with, other components. It isto be understood that such depicted architectures are merely exemplary,and that in fact many other architectures can be implemented whichachieve the same functionality. In a conceptual sense, any arrangementof components to achieve the same functionality is effectively“associated” such that the desired functionality is achieved. Hence, anytwo components herein combined to achieve a particular functionality canbe seen as “associated with” each other such that the desiredfunctionality is achieved, irrespective of architectures or intermedialcomponents. Likewise, any two components so associated can also beviewed as being “connected” or “coupled” to each other to achieve thedesired functionality, and any two components capable of being soassociated can also be viewed as being “couplable” to each other toachieve the desired functionality. Specific examples of couplableinclude but are not limited to physically interactable and/or physicallyinteracting components and/or wirelessly interactable and/or wirelesslyinteracting components and/or logically interactable and/or logicallyinteracting components.

It is believed that the present disclosure and many of its attendantadvantages will be understood by the foregoing description, and it willbe apparent that various changes may be made in the form, construction,and arrangement of the components without departing from the disclosedsubject matter or without sacrificing all of its material advantages.The form described is merely explanatory, and it is the intention of thefollowing claims to encompass and include such changes. Furthermore, itis to be understood that the invention is defined by the appendedclaims.

What is claimed:
 1. A system comprising: an illumination source togenerate an illumination beam; one or more illumination optics to directthe illumination beam to a sample at an off-axis angle along anillumination direction; one or more collection optics to collectscattered light from the sample in response to the illumination beam ina dark-field mode; a phase mask located at a first pupil plane of theone or more collection optics, wherein the phase mask is configured toprovide different phase shifts for light in two or more pupil regions ofa collection area to reshape a point spread function of light scatteredfrom one or more particles on a surface of the sample, wherein thecollection area corresponds to a numerical aperture of the one or morecollection optics; a polarization rotator located at a second pupilplane of the one or more collection optics, wherein the polarizationrotator provides a spatially-varying polarization rotation angleselected to rotate light scattered from the surface of the sample to aselected polarization angle, wherein the polarization rotator includesan optically-active material with an optic axis oriented perpendicularto the second pupil plane that rotates a polarization of light in thesecond pupil plane based on optical activity, wherein theoptically-active material has a spatially-varying thickness across thepupil plane to rotate the light scattered from the surface of the sampleto the selected polarization angle; a polarizer aligned to reject lightpolarized along the selected polarization angle; and a detector togenerate a dark-field image of the sample based on light passed by thepolarizer, wherein the light passed by the polarizer includes at least aportion of the light scattered by the one or more particles on thesurface of the sample.
 2. The system of claim 1, wherein the phase maskis located prior to the polarization rotator.
 3. The system of claim 1,wherein the phase mask reshapes the point spread function of lightscattered from the one or more particles on the surface of the sample toprovide a central peak in the point spread function.
 4. The system ofclaim 1, wherein the first pupil plane and the second pupil plane areconjugate planes.
 5. The system of claim 1, wherein the first pupilplane and the second pupil plane are a common pupil plane.
 6. The systemof claim 1, wherein the two or more pupil regions comprise: a first halfof the collection area and a second half of the collection area dividedalong the illumination direction.
 7. The system of claim 6, wherein afirst segment of the phase mask comprises: a half-wave plate coveringthe first half of the collection area.
 8. The system of claim 7, whereinthe half-wave plate is oriented to provide a 7 phase shift along adirection in the pupil plane corresponding to an angle that isorthogonal to a plane of incidence of the illumination beam on thesample.
 9. The system of claim 7, wherein a second segment of the phasemask comprises: a compensator plate formed from an optically homogenousmaterial along a propagation direction covering the second half of thecollection area, wherein an optical path of light through thecompensator corresponds to an optical path of light through thehalf-wave plate within a selected tolerance.
 10. The system of claim 7,wherein a second segment of the phase mask comprises: an aperturecovering the second half of the collection area.
 11. The system of claim10, wherein the half-wave plate is tilted to at least partiallycompensate for optical path differences between light travelling throughthe first and second halves of the collection area.
 12. An apparatuscomprising: a polarization rotator providing a spatially-varyingpolarization rotation angle selected to rotate light scattered from asurface of a sample to a selected polarization angle when thepolarization rotator is placed in a pupil plane of an imaging system,wherein the light scattered from the surface of the sample propagatesthrough the polarization rotator along a thickness direction, whereinthe polarization rotator includes an optically-active material with anoptic axis oriented along the thickness direction that rotates apolarization of light based on optical activity, wherein theoptically-active material has a spatially-varying thickness across atransverse direction orthogonal to the thickness direction to rotate thelight scattered from the surface of the sample to the selectedpolarization angle.
 13. The apparatus of claim 12, wherein thespatially-varying thickness across the pupil plane of the polarizationrotator varies with a one-dimensional spatial distribution.
 14. Theapparatus of claim 12, wherein the spatially-varying thickness acrossthe pupil plane of the polarization rotator varies with atwo-dimensional spatial distribution.
 15. The apparatus of claim 12,wherein the spatially-varying thickness across the pupil plane of thepolarization rotator varies monotonically.
 16. The apparatus of claim12, wherein the spatially-varying thickness across the pupil plane ofthe polarization rotator has a symmetric distribution with respect tocenter of the polarization rotator.
 17. The apparatus of claim 12,wherein the optically-active material comprises: an optically-activecrystal having an optic axis oriented perpendicular to the pupil plane.18. A system comprising: an illumination source to generate anillumination beam; one or more illumination optics to direct theillumination beam to a sample at an off-axis angle along an illuminationdirection; one or more collection optics to collect scattered light fromthe sample in response to the illumination beam in a dark-field mode; aphase mask located at a first pupil plane of the one or more collectionoptics, wherein the phase mask is configured to provide different phaseshifts for light in two or more pupil regions of a collection area toreshape a point spread function of light scattered from one or moreparticles on a surface of the sample, wherein the collection areacorresponds to a numerical aperture of the one or more collectionoptics; a polarization rotator located at a second pupil plane of theone or more collection optics, wherein the polarization rotator providesa spatially-varying polarization rotation angle selected to rotate lightscattered from the surface of the sample to a selected polarizationangle, wherein the polarization rotator includes an angularly-segmentedhalf-wave plate including a plurality of segments having edges orientedto intersect at an apex point in the second pupil plane, wherein theapex point corresponds to specular reflection of the illumination beamin the second pupil plane; a polarizer aligned to reject light polarizedalong the selected polarization angle; and a detector to generate adark-field image of the sample based on the light passed by thepolarizer, wherein the light passed by the polarizer includes at least aportion of light scattered by the one or more particles on the surfaceof the sample.
 19. The system of claim 18, wherein the phase mask islocated prior to the polarization rotator.
 20. The system of claim 18,wherein the phase mask reshapes the point spread function of lightscattered from the one or more particles on the surface of the sample toprovide a central peak in the point spread function.
 21. The system ofclaim 18, wherein the first pupil plane and the second pupil plane areconjugate planes.
 22. The system of claim 18, wherein the first pupilplane and the second pupil plane are a common pupil plane.
 23. Thesystem of claim 18, wherein the two or more pupil regions comprise: afirst half of the collection area and a second half of the collectionarea divided along the illumination direction.
 24. The system of claim23, wherein a first segment of the phase mask comprises: a half-waveplate covering the first half of the collection area.
 25. The system ofclaim 24, wherein the half-wave plate is oriented to provide a 7 phaseshift along a direction in the pupil plane corresponding to an anglethat is orthogonal to a plane of incidence of the illumination beam onthe sample.
 26. The system of claim 24, wherein a second segment of thephase mask comprises: a compensator plate formed from an opticallyhomogenous material along a propagation direction covering the secondhalf of the collection area, wherein an optical path of light throughthe compensator corresponds to an optical path of light through thehalf-wave plate within a selected tolerance.
 27. The system of claim 24,wherein a second segment of the phase mask comprises: an aperturecovering the second half of the collection area.
 28. The system of claim27, wherein the half-wave plate is tilted to at least partiallycompensate for optical path differences between light travelling throughthe first and second halves of the collection area.
 29. The system ofclaim 18, wherein the one or more illumination optics are configured todirect the illumination beam to the sample with a p-polarization. 30.The system of claim 18, wherein the polarizer comprises: a polarizingbeamsplitter, wherein the polarizing beamsplitter directs the scatteredlight from the sample passed by the polarizer along a first opticalpath, wherein the polarizing beamsplitter directs the scattered lightfrom the sample rejected by the polarizer along a second optical pathdifferent than the first optical path.
 31. The system of claim 30,further comprising: an additional detector configured to generate adark-field image of the sample based on the scattered light from thesample rejected by the polarizer along the second optical path, whereinthe scattered light from the sample rejected by the polarizer includeslight scattered by the surface of the sample within a selected rejectiontolerance.
 32. The system of claim 18, wherein the light scattered fromthe surface of the sample has a known electric field distribution,wherein the polarization rotator is configured to rotate light polarizedwith the known electric field distribution to the selected polarizationangle.
 33. A system comprising: an illumination source to generate anillumination beam; one or more illumination optics to direct theillumination beam to a sample at an off-axis angle along an illuminationdirection; a detector; one or more collection optics to generate adark-field image of the sample on the detector based on light collectedfrom the sample in response to the illumination beam; a phase masklocated at a pupil plane, wherein the phase mask is configured toprovide different phase shifts for light in two or more pupil regions ofa collection area to reshape a point spread function of light scatteredfrom one or more particles on a surface of the sample, wherein thecollection area corresponds to a numerical aperture of the one or morecollection optics; and a linearly-segmented polarizer including aplurality of segments distributed in a pupil plane of the one or morecollection optics along a segmentation direction, wherein a rejectionaxis of each segment is oriented to reject light scattered from thesurface of the sample within the segment.
 34. The system of claim 33,wherein the rejection axis of each segment is oriented to reject thelight scattered from the surface of the sample within the segment basedon a known electric field distribution of light scattered from thesurface of a sample in response to illumination with a knownpolarization at a known incidence angle.
 35. The system of claim 34,wherein the known polarization is p-polarization.
 36. The system ofclaim 33, wherein the plurality of segments are linearly distributedalong a direction perpendicular to the illumination direction.
 37. Thesystem of claim 33, wherein the phase mask reshapes the point spreadfunction of light scattered from one or more particles on the sample toprovide a central peak in the point spread function.
 38. The system ofclaim 33, wherein the two or more pupil regions comprise: a first halfof the collection area and a second half of the collection area dividedalong the illumination direction.
 39. The system of claim 38, wherein afirst segment of the phase mask comprises: a half-wave plate coveringthe first half of the collection area.
 40. The system of claim 39,wherein the half-wave plate is oriented to provide a 7 phase shift alonga direction in the pupil plane corresponding to an angle that isorthogonal to a plane of incidence of the illumination beam on thesample.
 41. The system of claim 39, wherein a second segment of thephase mask comprises: a compensator plate formed from an opticallyhomogenous material along a propagation direction covering the secondhalf of the collection area, wherein an optical path of light throughthe compensator corresponds to an optical path of light through thehalf-wave plate within a selected tolerance.
 42. The system of claim 39,wherein a second segment of the phase mask comprises: an aperturecovering the second half of the collection area.
 43. The system of claim42, wherein the half-wave plate is tilted to at least partiallycompensate for optical path differences between light travelling throughthe first and second halves of the collection area.